Semantic memory plays a critical role in communication and thought, but advances in the cognitive and neural basis for semantic memory have proven elusive. We propose a novel approach to semantic memory by focusing on generalized quantifiers like "some of the apples" and "most of the oranges." Our model of generalized quantifier comprehension includes at least a finite set of simple circuits that represent number knowledge, a working memory device the retains the results of intermediate computations, and a small set of combinatorial operations that manipulate information held in working memory. We map this semantic domain onto a large-scale neural network that includes at least parietal cortex (for number knowledge), inferior frontal cortex (for working memory), and dorsolateral prefrontal cortex (for executive switching). Preliminary computational work, behavioral studies in healthy seniors and patients with focal neurodegenerative diseases, and functional neuroimaging work support these distinctions. Patients with corticobasal degeneration have a fundamental deficit in number knowledge but little other lexical comprehension difficulty, related to parietal atrophy. They are particularly impaired in their comprehension of "first-order quantifiers" like "some of the X" that depend crucially on number knowledge; fMRI work in healthy adults relates comprehension of first-order quantifiers to parietal cortex. Frontotemporal dementia and Alzheimer's disease patients have limited working memory and poor switching that are associated with frontal atrophy. They are impaired in their comprehension of "higher-order quantifiers" like "most of the X" that, beyond number knowledge, also require working memory and the manipulation of information retained in working memory, fMRI work in healthy adults relates comprehension of higher-order quantifiers to frontal cortex. We propose additional modeling, behavioral, and functional neuroimaging studies in healthy seniors and patients with these neurodegenerative diseases to establish the cognitive and neural contribution of number knowledge, working memory, and executive switching during generalized quantifier comprehension. The results of these studies will provide a novel and important perspective on the neural basis for semantic memory, and will improve diagnostic and prognostic accuracy in patients suffering from dementia. [unreadable] [unreadable]